Question

Пожалуйста решите с подробным объяснением

Answer 1

Значит x+y²=x²+y;
           x²-x=y²-y;
           x(x-1)=y(y-1);
       если x>y то
(x-1)>(y-1) u x>y ⇒x(x-1)>y(y-1)
значит х>y не подходит
   если x<y то
(x-1)<(y-1) u x<y ⇒x(x-1)<y(y-1)
значит х<y не подходит

тогда х=у
y+y²=3
y²+y-3=0
D=1+4*3=13
y=(-1+√13)/2=x
y=(-1-√13)/2=x

Answer 2

Amazon EC2 T4g Instances

Amazon EC2 T4g instances are a type of virtual server offered by Amazon Web Services (AWS). These instances are powered by AWS Graviton2 processors, which are custom-designed by AWS and based on the Arm architecture. T4g instances are optimized for a balance of performance and cost-effectiveness.

T4g instances are suitable for a wide range of workloads, including microservices, small databases, and development environments. They offer a good price-to-performance ratio and are well-suited for applications that don't require high levels of compute power.

The T4g instance family includes different instance sizes, such as t4g.nano, t4g.micro, t4g.small, and t4g.medium. Each instance size has different specifications in terms of CPU, memory, and network performance.

For example, the t4g.small instance size offers 2 vCPUs, 2 GB of memory, and up to 750 Mbps of network bandwidth. It is a cost-effective option for small-scale workloads.

To launch an Amazon EC2 T4g instance, you can use the AWS Management Console, AWS Command Line Interface (CLI), or AWS SDKs. You can choose the desired instance size, configure networking and storage options, and launch the instance in your preferred AWS region.

[[3]](https://aws.amazon.com/ru/ec2/faqs/)

GCC Compiler Options

GCC (GNU Compiler Collection) is a popular open-source compiler system used for compiling and building software programs. It supports multiple programming languages, including C, C++, and Fortran.

GCC provides various compiler options that allow developers to customize the compilation process and optimize the generated code. Some commonly used GCC compiler options include:

- -mtune: This option specifies the target microarchitecture for code optimization. It allows developers to tune the generated code for a specific CPU model or architecture. - -mcpu: Similar to -mtune, this option specifies the target CPU model for code optimization. It is used to generate code specifically for a particular CPU. - -march: This option specifies the target architecture for code generation. It allows developers to generate code for a specific CPU architecture, such as x86 or x86-64. - -O: This option enables optimization of the generated code. It includes different optimization levels, such as -O1, -O2, -O3, and -Ofast, with each level providing increasing levels of optimization.

These compiler options can be used to improve the performance and efficiency of compiled programs by tailoring the code generation process to the target hardware.

For example, the -march=native option instructs GCC to generate code optimized for the native architecture of the machine on which the compilation is performed. This can result in improved performance for the specific hardware configuration.

To use these GCC compiler options, you can specify them as command-line arguments when invoking the GCC compiler. For example:

gcc -mtune=generic -march=x86-64 -O3 -o output_file input_file.c

This command compiles the input_file.c source file using the specified compiler options and generates the output_file executable.

HeapSort Algorithm

HeapSort is a comparison-based sorting algorithm that uses a binary heap data structure to sort elements. It is an in-place sorting algorithm, meaning it does not require additional memory beyond the input array.

The algorithm works by first building a max-heap from the input array. A max-heap is a complete binary tree where the value of each node is greater than or equal to the values of its children. Once the max-heap is constructed, the largest element (root of the heap) is swapped with the last element of the array. The heap size is then reduced by one, and the heapify operation is performed on the root to maintain the max-heap property. This process is repeated until the entire array is sorted.

Here is a step-by-step example of the HeapSort algorithm:

1. Given an input array: [4, 10, 3, 5, 1] 2. Build a max-heap from the array: [10, 5, 3, 4, 1] 3. Swap the root (10) with the last element (1) and reduce the heap size: [1, 5, 3, 4, 10] 4. Perform heapify on the root: [5, 4, 3, 1, 10] 5. Swap the root (5) with the last element (1) and reduce the heap size: [1, 4, 3, 5, 10] 6. Perform heapify on the root: [4, 1, 3, 5, 10] 7. Swap the root (4) with the last element (3) and reduce the heap size: [3, 1, 4, 5, 10] 8. Perform heapify on the root: [3, 1, 4, 5, 10] 9. Swap the root (3) with the last element (1) and reduce the heap size: [1, 3, 4, 5, 10] 10. Perform heapify on the root: [1, 3, 4, 5, 10] 11. The array is now sorted: [1, 3, 4, 5, 10]

HeapSort has a time complexity of O(n log n) in the average and worst cases, where n is the number of elements in the input array. It is considered an efficient sorting algorithm and is often used in practice.

PHP Session Management

In PHP, sessions are used to store and manage user-specific data across multiple requests. Sessions allow you to store variables that can be accessed and modified throughout a user's browsing session on a website.

To start a session in PHP, you need to call the `session_start()` function at the beginning of your script. This function initializes a session or resumes an existing one.

Once a session is started, you can store data in the `$_SESSION` superglobal array. This array is accessible across different pages of your website as long as the session is active. You can store any type of data in the `$_SESSION` array, including strings, numbers, arrays, and objects.

For example, to store a value in the session:

$_SESSION['username'] = 'John';

To retrieve the stored value in another script:

echo $_SESSION['username']; // Output: John

To destroy a session and remove all session data, you can use the `session_destroy()` function. This function terminates the current session and deletes the session cookie. However, it does not unset the `$_SESSION` superglobal array. To completely unset the session variables, you can use the `session_unset()` function.

PHP sessions can be configured using the `php.ini` file. Some common session-related configuration options include:

- `session.use_trans_sid`: This option determines whether PHP appends the session ID to URLs when cookies are disabled. Setting it to 0 disables this behavior for security reasons. - `session.use_only_cookies`: This option specifies whether PHP uses only cookies to store the session ID. Setting it to 1 ensures that the session ID is only transmitted via cookies. - `session.save_path`: This option sets the directory where session data is stored on the server. By default, PHP uses the system's default temporary directory.

It's important to handle sessions securely to prevent session hijacking or session fixation attacks. This can be achieved by using secure session management practices, such as regenerating session IDs after successful login, using secure cookies, and properly configuring session-related options.

Longest Common Subsequence (LCS) Problem

The Longest Common Subsequence (LCS) problem is a classic computer science problem that involves finding the longest subsequence that is common to two or more sequences. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

For example, given two sequences "abcde" and "ace", the longest common subsequence is "ace" with a length of 3.

The LCS problem has applications in various fields, including bioinformatics, text comparison, and version control systems. It is often solved using dynamic programming techniques.

The dynamic programming approach to solving the LCS problem involves building a table to store the lengths of the longest common subsequences for different prefixes of the input sequences. The table is filled in a bottom-up manner, starting from the smallest subproblems and gradually building up to the larger subproblems.

Here is a high-level overview of the dynamic programming algorithm for the LCS problem:

1. Create a table with dimensions (m+1) x (n+1), where m and n are the lengths of the input sequences. 2. Initialize the first row and first column of the table to 0. 3. Iterate over the remaining cells of the table in row-major order. 4. If the characters at the corresponding positions in the input sequences match, set the value of the current cell to the value of the cell diagonally above-left plus 1. 5. Otherwise, set the value of the current cell to the maximum of the cell above or the cell to the left. 6. The value in the bottom-right cell of the table represents the length of the longest common subsequence. 7. To reconstruct the longest common subsequence, start from the bottom-right cell and backtrack through the table, following the rules used to fill the table.

The time complexity of the dynamic programming algorithm for the LCS problem is O(mn), where m and n are the lengths of the input sequences. The space complexity is also O(mn) to store the table.

The LCS problem can be extended to find the actual longest common subsequence, rather than just its length. This can